Relation between boltsmann/gas constant and temperature

[negative]

so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation :
PV=nRT is true.
i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird.
each molocule should be only deflected in the direction that the wall is hitting it and so each molecule hits all walls (expect the one that exactly moves parallel to the wall) and each one has effect on the pressure.
but from what i see in books, my way only works, if i assume that each molecule gets deflected exactly in opposite of it's own direction, so only one third of the molecules interact with the selected wall.
my question is that is there any sort of "evidence" that shows proves the constant multiplications of the relation between boltsmann constant and average kinetic energy of a molecule in an ideal gas which is
E=(3/2)kT ?
is there any evidence for that (3/2) or it's just purely theoretical?

 

[Nguyen Son]

About the number 3/2, you can calculate it if you've learned Statistical Mechanics course
Actually, I knew that E=(3/2)kT when I study Thermodynamics course, but we just admitted, I didn't know why we have it, until I studied Stat. mechanics

 

[negative]

About the number 3/2, you can calculate it if you've learned Statistical Mechanics course
Actually, I knew that E=(3/2)kT when I study Thermodynamics course, but we just admitted, I didn't know why we have it, until I studied Stat. mechanics

well , it is highly likely that i don't know what i am talking about, but statistics doesn't give stuff out of nowhere. it calculates the result based on the model that you describe for it.
i just read the meaning of the degree of freedom. i can easily understand that the degrees of freedom in the equation
V_rms²=V_x²+V_y²V_z²
are V_x,V_y and V_z .i understand easily when i try to solve it this way. i have done it before many times. including the first times without having the knowledge.
but i wanted to do it spherical. and dang. after about 24 hour of thinking i finally found out the issue of my distribution. honestly you don't need complicated sentences to understand these kind of simple distribution. it's just about learning to think the right way. which is why i don't give up. i want to learn to think the right way.
the issue of my calculations was the fact that i considered slots for molecules based on spherical coordinates and i was offering the same amount of slots for circles with different radiuses. and the result was uneven distribution.
now i know i don't know how to define even distribution in spherical coordinates. which helps me avoid mistakes

thanks for the comment though, but i never do what you do. that's why changed physics to programming. i cannot pass if i can't give up on things that i care about. i don't have much time to study physics now but when i do, i roam free.